MEMO 2016 pojedinačno problem 4


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Find all functions f : \mathbb{N} \to \mathbb{N} such that f(a) + f(b) divides 2(a + b - 1) for all a, b \in \mathbb{N}.

Remark: \mathbb{N} = \{1, 2, 3, \ldots\} denotes the set of positive integers.

Source: Srednjoeuropska matematička olimpijada 2016, pojedinačno natjecanje, problem 4